Details

sample342.0ms

Algorithm

intervals

Results

72.0ms	157×	body	80	valid
45.0ms	358×	body	80	nan
18.0ms	32×	body	1280	valid
14.0ms	34×	body	640	valid
10.0ms	18×	body	1280	nan
9.0ms	21×	body	640	nan
7.0ms	20×	body	320	valid
3.0ms	11×	body	320	nan
3.0ms	13×	body	160	valid
1.0ms	6×	body	160	nan

simplify4.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
7	4703
6	1985
5	1092
4	526
3	232
2	100
1	41
0	18

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.0b

localize67.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
0.5b	(* (sqrt 2.0) t)
13.1b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
19.5b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite169.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
13×	`sqrt-prod`
12×	`*-un-lft-identity` `add-cube-cbrt`
11×	`add-cbrt-cube` `add-exp-log`
7×	`pow1`
6×	`associate-/r` `times-frac` `associate-l*` `add-log-exp`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u`
3×	`flip3--` `associate-r` `flip--`
2×	`cbrt-undiv` `div-exp` `prod-exp` `associate--l+` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`distribute-rgt-in` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `-commutative` `div-inv` `associate-/l`

Counts

4 → 90

Calls

4 calls:

68.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
9.0ms	(* (sqrt 2.0) t)
28.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
58.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series2.9s

Counts

4 → 12

Calls

4 calls:

683.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
60.0ms	(* (sqrt 2.0) t)
331.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
1.8s	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify2.8s

Counts

102 → 102

Iterations

Iter	Nodes
done	5002
2	2749
1	482
0	178

prune888.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 2.3b

localize48.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt 2.0) t)
1.0b	(fma t t (/ l (/ x l)))
4.4b	(fma (/ t (/ x t)) 4.0 (* 2.0 (fma t t (/ l (/ x l)))))
25.2b	(sqrt (fma (/ t (/ x t)) 4.0 (* 2.0 (fma t t (/ l (/ x l))))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`pow1` `sqrt-prod`
6×	`add-cbrt-cube` `associate-l` `add-exp-log`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-r`
2×	`fma-udef` `unswap-sqr`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 59

Calls

4 calls:

16.0ms	(* (sqrt 2.0) t)
1.0ms	(fma t t (/ l (/ x l)))
1.0ms	(fma (/ t (/ x t)) 4.0 (* 2.0 (fma t t (/ l (/ x l)))))
3.0ms	(sqrt (fma (/ t (/ x t)) 4.0 (* 2.0 (fma t t (/ l (/ x l))))))

series519.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(* (sqrt 2.0) t)
62.0ms	(fma t t (/ l (/ x l)))
129.0ms	(fma (/ t (/ x t)) 4.0 (* 2.0 (fma t t (/ l (/ x l)))))
275.0ms	(sqrt (fma (/ t (/ x t)) 4.0 (* 2.0 (fma t t (/ l (/ x l))))))

simplify911.0ms

Counts

71 → 71

Iterations

Iter	Nodes
done	5000
2	786
1	204
0	102

prune656.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.3b

localize59.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* (cbrt (sqrt 2.0)) t))
1.0b	(fma t t (/ l (/ x l)))
4.4b	(fma (/ t (/ x t)) 4.0 (* 2.0 (fma t t (/ l (/ x l)))))
25.2b	(sqrt (fma (/ t (/ x t)) 4.0 (* 2.0 (fma t t (/ l (/ x l))))))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

17×	`pow1`
16×	`add-exp-log`
10×	`add-cbrt-cube`
8×	`pow-prod-down` `prod-exp` `cbrt-unprod`
6×	`add-sqr-sqrt`
5×	`*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-prod`
2×	`fma-udef`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r` `associate-l` `*-commutative`

Counts

4 → 59

Calls

4 calls:

78.0ms	(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* (cbrt (sqrt 2.0)) t))
0.0ms	(fma t t (/ l (/ x l)))
1.0ms	(fma (/ t (/ x t)) 4.0 (* 2.0 (fma t t (/ l (/ x l)))))
3.0ms	(sqrt (fma (/ t (/ x t)) 4.0 (* 2.0 (fma t t (/ l (/ x l))))))

series496.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* (cbrt (sqrt 2.0)) t))
83.0ms	(fma t t (/ l (/ x l)))
108.0ms	(fma (/ t (/ x t)) 4.0 (* 2.0 (fma t t (/ l (/ x l)))))
233.0ms	(sqrt (fma (/ t (/ x t)) 4.0 (* 2.0 (fma t t (/ l (/ x l))))))

simplify1.2s

Counts

71 → 71

Iterations

Iter	Nodes
done	5000
2	968
1	246
0	108

prune648.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 2.3b

localize83.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) t))
1.0b	(fma t t (/ l (/ x l)))
4.4b	(fma (/ t (/ x t)) 4.0 (* 2.0 (fma t t (/ l (/ x l)))))
25.2b	(sqrt (fma (/ t (/ x t)) 4.0 (* 2.0 (fma t t (/ l (/ x l))))))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

12×	`sqrt-prod`
10×	`pow1`
9×	`add-sqr-sqrt` `add-cbrt-cube` `associate-l` `add-exp-log`
8×	`*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`fma-udef`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r` `*-commutative`

Counts

4 → 61

Calls

4 calls:

34.0ms	(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) t))
0.0ms	(fma t t (/ l (/ x l)))
0.0ms	(fma (/ t (/ x t)) 4.0 (* 2.0 (fma t t (/ l (/ x l)))))
2.0ms	(sqrt (fma (/ t (/ x t)) 4.0 (* 2.0 (fma t t (/ l (/ x l))))))

series507.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) t))
62.0ms	(fma t t (/ l (/ x l)))
109.0ms	(fma (/ t (/ x t)) 4.0 (* 2.0 (fma t t (/ l (/ x l)))))
270.0ms	(sqrt (fma (/ t (/ x t)) 4.0 (* 2.0 (fma t t (/ l (/ x l))))))

simplify1.6s

Counts

73 → 73

Iterations

Iter	Nodes
done	5000
2	895
1	233
0	109

prune589.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 2.2b

regimes1.1s

Accuracy

77.4% (5.4b remaining)

Error of 9.3b against oracle of 3.9b and baseline of 27.8b

bsearch996.0ms

Steps

Iters	Range		Point
9	8.029604051112713e+47	4.771574953324125e+55	4.214549585149478e+55
10	3.1913228427846884e-157	3.080469255526081e-145	3.2479806443803153e-157
10	7.396249846299801e-250	6.414192999540213e-240	1.8396588411989053e-241
9	-2.2008797770019196e+94	-2.884593901536308e+87	-1.940005881918409e+94

simplify47.0ms

Iterations

Iter	Nodes
done	63
3	63
2	60
1	57
0	49

end0.0ms

sample6.1s

Algorithm

intervals

Results

1.4s	9922×	body	80	nan
1.0s	1060×	body	640	valid
905.0ms	819×	body	1280	valid
612.0ms	5112×	body	80	valid
381.0ms	599×	body	1280	nan
243.0ms	644×	body	320	valid
235.0ms	625×	body	640	nan
96.0ms	335×	body	320	nan
79.0ms	191×	body	160	nan
71.0ms	365×	body	160	valid